Prsentation PowerPoint

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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
F. Lelong, M. Gradeck, D. Maillet, N. Seiler, G.
Repetto
SHF, Grenoble, Sept 8-9, 2008
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Content

• General background
• Experimental set-up conditions
• Direct heat transfer problem
• Inverse heat transfer problem
• Conclusions and perspectives

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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
GENERAL BACKGROUND cooling of ballooned region
during a LOCA
Significant blockage of a part in the core
Thermo-hydraulics effects in the ballooned area
during the reflooding phase.
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
GENERAL BACKGROUND Droplet impinging a hot slab
Three possible impact regimes
Ts 400 C R 0,05 mm V 8 m/s Nickel slab
Ts120 C, R 0,075 mm, V5,2 m/s
Ts250 C, R 0,055 mm, V7,2 m/s
Dimensionless numbers
LOCA

• In LOCA situation
• low velocity (2 to 6 m/s)
• Low diameter (80 to 200 mm)
• Temperature gtgt Leidenfrost Temperature
  

Bouncing regime
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
EXPERIMENTAL SET-UP
EXPERIMENTAL CONDITIONS

• Stream of water droplets
• Diameter 80µm to 200µm.
• Velocity 2 m/s to 5m/s,

• Slab
• Nickel, T600-800C,
• Diameter 25 mm, thickness 250 to 500 µm,
• Variable incident angle

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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Inverse methods Estimation of the cooling flux.
Basic process of inversion
Minimization of the difference between results
from a theoretical model and results from
measurements (knowing that each result can be
 noise )
Estimated cooling flux
Theoritical cooling flux
XBYexp
X
Heat equation Model
Least square operator
Direct heat transfer problem
Inverse heat transfer problem
A
Regularization
Rear face temperatures
Measurements
Yexp
YAX
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Direct heat transfer problem Presentation.
Two dimensional modelling bouncing droplet
e 0.5 mm D 2 cm R 50 µm

• Assuming a axisymmetric cooling flux q(r,t)

• An uniform flux distribution on the 0R
  interval and on the 0,t1

With t1 the resident time of the droplet into the
slab and R the droplet radius
Sensible heat
Latent heat
With H the heaviside function, Sg the droplet
surface
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Direct heat transfer problem Resolution.
Writing the heat equation as follow
Using the Hankel transform in space and the
Laplace Transform in time
With
Solution by the quadripole method, at the rear
face (ze) is
With
and
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Direct heat transfer problem Resolution.
Laplace inversion leads to a convolution product
With f(t) the original of F(p)
Return to the time-space domain yields
With Jn the n-order modified Bessel function
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Direct heat transfer problem Results.
rear face responses one single impact and 10
successive impacts
Rear face response One single impact (R 50
?m, e 0.5 mm)
Rear face response 10 successive impacts (R
50 ?m, e 0.5 mm)
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Direct heat transfer problem Results.
Rear face responses 10 successive impacts with
different frequency

• The 1D characteristic diffusion time

with
Evaluation of the injection frequency effect (R
50 µm, e 0,5 mm)
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Inverse heat transfer problem Resolution
Equation in Hanckel domain starting point of
the inversion heat conduction problem
The time integral is estimated by a trapezium
rule and in a matrix formulation
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Inverse heat transfer problem Resolution
Calculation of the Hankel transform of the
experimental temperatures
At t fixed
It yields
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Inverse heat transfer problem Results.
With the numbers of harmonics finds minimizing
the error function
Evaluation of the injection frequency effect (R
50 µm, e 0,5 mm)
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ESTIMATION OF DROPLETS/WALL HEAT TRANSFER UNDER
LOCA CONDITIONS IN A PWR
Conclusion
Perspectives